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Existence of quasiregular mappings

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Holomorphic Functions and Moduli I

Part of the book series: Mathematical Sciences Research Institute Publications ((MSRI,volume 10))

Abstract

Quasiregular mappings are roughly quasiconformal mappings without the homeomorphism requirement. In the Euclidean n-space R n, n ≥ 2, the definition is given as follows. A continuous map f: G → R n of a domain G in R n is called quasiregular (qr) if (1) f is in the local Sobolev space W 1n,loc (G), i-.e. f has weak order partial derivatives which are locally in L n, and (2) there exists K, 1 ≤ K < ∞, such that

$$ {\left| {f\prime (x)} \right|^{n}}K{J_{f}}(x)a.e. $$
(1.1)

.

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References

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Author information

Authors and Affiliations

  1. Department of Mathematics, University of Helsinki, 00100, Helsinki, Finland

    Seppo Rickman

Authors
  1. Seppo Rickman
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Editor information

Editors and Affiliations

  1. Department of Mathematics, Purdue University, West Layfayete, IN, 47909, USA

    D. Drasin

  2. Department of Mathematics, State University of New York at Stony Brook, Stony Brook, NY, 11794, USA

    I. Kra

  3. Department of Mathematics, Cornell University, Ithaca, NY, 14853, USA

    C. J. Earle

  4. Department of Mathematics, University of Minnesota, Minneapolis, MN, 55455, USA

    A. Marden

  5. Department of Mathematics, University of Michigan, Ann Arbor, MI, 48109, USA

    F. W. Gehring

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© 1988 Springer-Verlag New York Inc.

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Rickman, S. (1988). Existence of quasiregular mappings. In: Drasin, D., Kra, I., Earle, C.J., Marden, A., Gehring, F.W. (eds) Holomorphic Functions and Moduli I. Mathematical Sciences Research Institute Publications, vol 10. Springer, New York, NY. https://doi.org/10.1007/978-1-4613-9602-4_15

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  • DOI: https://doi.org/10.1007/978-1-4613-9602-4_15

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4613-9604-8

  • Online ISBN: 978-1-4613-9602-4

  • eBook Packages: Springer Book Archive

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